The creation of a simplified mathematical model of a controlled technology is generally the first step in control system monitoring, diagnostics, or real time optimization system design. A system's success greatly depends on model accuracy and reliability. Whereas the controller or optimizer algorithms are usually generic, well tested and then reused across multiple applications, the models usually have to be created or calibrated anew with each application. For example, a passenger car engine control unit will not work correctly in a different car model with a different engine type, though the control algorithm can actually be identical. Model creation and calibration represents a bottleneck within control system design. For many modem model based control approaches, the model is in fact the main parameter (apart from penalties and constraints) which parameterizes a generic controller for the given application.
Most reliable models are obtained from the first principles: mechanical, thermodynamic, chemical, and other laws. Such models naturally obey the mass or energy conservation laws, etc. Any such law imposes additional constraint on the identification problem thus eliminating uncertainty of the problem (often equivalent to the number of unknowns). Consequently, first principle models can be calibrated using smaller data sets compared to the data sets required for purely empirical black box models (i.e. a model of a system for which there is no a priori information available). Typically, the first principle models exhibit greater prediction error towards the data set used for the calibration when compared to the black box models. But the opposite is usually true when comparing the model prediction accuracy on a data set not used for the calibration (i.e. extrapolating the model behavior further from the calibration data). Models derived from the first principles can still have a number of unknown parameters. To identify their values is called the “grey box identification problem” (to distinguish it from the black box identification, where the model structure is arbitrary and not derived from the physical laws).
There are two approaches to the grey box model identification of complex large scale nonlinear systems: local method and global method. Utilizing the local method, individual components (blocks or subsystems in the block diagrammatic representation) are fitted separately using their local input and output data, whereas in the global method all components are fitted simultaneously while always evaluating the predictions of the whole system. The global method can begin with local identification and then use the results as the initial condition for the global method. There are advantages to both approaches. For example, the local method has better convergence properties while the global method is statistically more efficient. Therefore, the inventors believe a need exists for a new method which combines advantages of both in addition to providing additional benefits.